2012/01/27 by Mauro Di Nasso, Di Nasso, Mauro
Mathematics · #03H05 #11B05 #11B13 #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03H05 #msc:11B05 #msc:11B13
paper · pdf · doi:10.48550/arxiv.1201.5865
Revised in a few parts
openalex publication_date 2012/01/27 · arxiv created 2013/12/24 · arxiv updated 2013/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By using nonstandard analysis, we prove embeddability properties of difference sets A-B of sets of integers. (A set A is "embeddable" into B if every finite configuration of A has shifted copies in B.) As corollaries of our main theorem, we obtain improvements of results by I.Z. Ruzsa about intersections of difference sets, and of Jin's theorem (as refined by V. Bergelson, H. Fürstenberg and B. Weiss), where a precise bound is given on the number of shifts of A-B which are needed to cover arbitrarily large intervals.